JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If \(\alpha+\beta+\gamma=2 \pi\), then the system of equations \(x+(\cos \gamma) y+(\cos \beta) z=0\) \((\cos \gamma) x+y+(\cos \alpha) z=0\) \((\cos \beta) x+(\cos \alpha) y+z=0\) has :
- A no solution
- B infinitely many solution
- C exactly two solutions
- D a unique solution
Answer & Solution
Correct Answer
(B) infinitely many solution
Step-by-step Solution
Detailed explanation
\(\alpha+\beta+\gamma=2 \pi\) \(\left|\begin{array}{ccc}1 & \cos \gamma & \cos \beta \\ \cos \gamma & 1 & \cos \alpha \\ \cos \beta & \cos \alpha & 1\end{array}\right|\) \(=1+2 \cos \alpha \cdot \cos \beta \cdot \cos \gamma-\cos ^{2} \alpha-\cos ^{2} \beta-\cos ^{2} \gamma\)…
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